Abstract
Let R be a ring of algebraic integers of an algebraic number field F and let ( ) R GL G n ≤ be a finite group. In (11) was proved that the R-span of G is just the matrix ring () R M n of the matrices - n n × over R if and only if the Brauer reduction of n R modulo every prime is absolutely irreducible. In this paper, we show that () R M G n R = if and only if the Brauer reduction of n R modulo a finite number of primes is absolutely irreducible. Moreover, we give conditions for n, under which () R M n is a Schur ring.
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